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Local linear regression for functional data

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Abstract

We study a non-linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method and derive its asymptotic mean square error. Computations involve a linear inverse problem as well as a representation of the small ball probability of the data and are based on recent advances in this area.

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Authors and Affiliations

  1. Département de Mathématiques, CC 051, Université Montpellier 2, Place Eugène Bataillon, 34095, Montpellier Cedex 5, France

    A. Berlinet, A. Elamine & A. Mas

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  1. A. Berlinet
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  2. A. Elamine
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  3. A. Mas
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Correspondence to A. Mas.

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Berlinet, A., Elamine, A. & Mas, A. Local linear regression for functional data. Ann Inst Stat Math 63, 1047–1075 (2011). https://doi.org/10.1007/s10463-010-0275-8

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  • DOI: https://doi.org/10.1007/s10463-010-0275-8

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